Maybe you found this blog while searching for texts related to physics, maths and/or one of the scientists named Bernoulli. Though, every now and then, I might write about maths, the main scope concerns the world of chess problems - views, experiences, pleasures, moments of frustration (indeed!). In most cases, posts are about solving, constructing, enjoying chess compositions.

26 August 2011

I became quite curious when I read the announcement that, beginning with issue 110, there are some new columns in the Chess Informant. Among other new things, it now has a selection of chess problems prepared by the International Solving Grandmaster and Grandmaster of chess compositions Milan Velimirovic. They not only want to offer problems for solving, but also intend "to bring insights from the professional point of view into the secrets of the chess problem world".

The other day, I could use the opportunity to have a look at the selected studies and problems and I looked forward to the promised insights.

Velimirovic summarizes the five World championships in chess composition. These competitions cover three year periods, starting with the years 1989 to 1991 for the first championship. He concentrates on the results in the three sections twomovers, threemovers, and moremovers. Thus, the reader is presented fifteen problems, each composed by the respective winner of a section.

I can only speak for the electronic edition which comes with a PGN file containing the problems. And what I saw there is not what I call professional. Naturally, each composition is stored as a game. But the result of all games is "0-1"!? Of course, that's totally wrong, as in orthodox mate problems it's always White who checkmates. The notation and annotations are not really sufficient to understand clearly what theme is shown and how, though its name and a brief description is given at the end of each virtual game. Moreover, there are obvious errors like an explanation mentioning the white queen, whereas there is none on the board at all!

Here is one of the awarded compositions that Velimirovic picked for the interested reader:

Anatoly Slesarenko

Championship of USSR 1991

1st Place

#2

(7+11)

This is the original notation for this problem:

I don't think the pattern of the theme is really made clear hereby. However, this table which I found here should help:

a

b

c

d

A,B

C

D

C,D

A

B

Applying it to the problem gives us a better picture:

Kxd3

cxd3

gxf3

Kxf3

1. Rd3? threats

Nf2, Qxd5

Qxf5

Ng5

1. Rf3! threats

Qxf5, Ng5

Nf2

Qxd5

Another renowned problemist takes care of the endgame studies: Yochanan Afek. Unfortunately, in a quite dry manner he simply shows nine diagrams without further comments.

The studies are also collected in a PGN file, each of them with lots of variations but no further text. Similar to the mate problems, the result tag of each virtual game does not show what you'd expect. I think "1-0" to indicate that White should win or "1/2-1/2" where White is to draw is common usage whereas here all games are marked with "Line". But that's the only thing to criticize. Now, there is one more sample for you:

19 August 2011

Admittedly, not all chess players nor all composers are actually thrilled by task problems. But I am. Therefore, I chose three more of them for you. And I think that you may like at least some of them.

The first three compositions feature the flight task which demands that in the diagram all eight flight squares for the king that is to be mated are accessible for him. No. 1 is sort of an extension of this task as the white king is even the only piece in a 6x7 area. The second problem demonstrates the task in a minimum of two moves. It's notable that the king is mated in the middle of the board and only one flight square is occupied. Finally, No. 3 shows an ideal mate with all four bishops after a series of checks and sacs of the heavy pieces.

Composition No. 7 pleases us with an alert black king. With each key move he visits another neighbouring square. Similarly, in the last problem the black king is checkmated on each of the eight adjacent squares.

12 August 2011

In the previous post I wrote about the famous 100 Dollar task and the Oudot task. Of course, there are several other challenges for composers of helpmate problems. I want to draw your attention to two of them.

The first one asks for the longest correct orthodox helpmate with no other black piece than the king and no promoted (white) piece. As far as I know, seven moves is still the maximum. There are already lots of h#6.5 which can be extended to a h#7 by forcing the black king to capture a white queen as first move leading to the actual diagram — see No. 1 where we could put the black king on h1 and add a wQh2. Moreover, dozens of "real" h#7 have been published and I picked two for you. Diagram 2 is an extraordinary problem using the complete set of white pieces. The third composition is also something special as it works without promotion.

Lots of attempts have been made but still nobody successfully extended the record to 7.5 or more moves yet. The only thing I know of: In 2004, Noam D. Elkies came up with a h#10 that had seven white bishops.

Compose a correct helpmate in more than 7 moves with black king solus and no promoted piece.

The second record to break is even more fascinating. I don't remember exactly how it happened, but while searching the Internet for interesting helpmates, I found a downloadable article in German that was published in the problem magazine harmonie in June 2006. It dealt with the quest for the longest helpmate. As with other tasks and records, several experts have tried a variety of constructions in vain. There were always duals or other flaws. Apparently, every now and then, some rather obscure (mainly) Russian problem chess media report on a new achievement, but in all cases a closer look reveals cooks. So far, nobody has been able to surpass the record that was established almost 80 years ago:

Compose a correct helpmate in more than 28 moves with no promoted pieces.

Surely, there aren't so many people being interested in helpmate records. But I hope there'll always be some problemists that still don't give up the search for a new record. Never forget Leonid Yarosh!

05 August 2011

Most probably you have heard of the Millennium Prize Problems. These are seven problems in mathematics that were stated by the Clay Mathematics Institute of Cambridge (CMI), Massachusetts, in 2000. The correct solution to any of them is awarded with a prize of 1,000,000 US dollars by the institute. In 2003, Grigori Perelman published a proof of the Poincaré conjecture. He was selected to receive the Fields Medal for this and awarded with the Millenium prize, but he declined both awards — it's quite interesting to read more about him and his work. Anyway, this is the only solved problem so far.

In mathematics, there are lots of such so far unsolved problems — and the same applies to chess compositions. We know several themes which composers all over the world and throughout the years still haven't been able to master. In the March 2006 issue of The Problemist Stephen Rothwell showed seven of those constructional challenges calling them "chess composing millennium problems". Until that time, no correct settings of the themes had yet been composed. Correct means correct and legal position, without promoted pieces. For each of them he stated a conjecture that it is unsolvable. Nevertheless, he offered a book credit of Euro 50 for any correct setting of one of the seven constructional challenges that he mentioned. Closing date was 31 December 2006. Unfortunately, I don't know about the results and I wonder how many entries he received at all ...

In 2010, the German composer Werner Keym published his first book "Eigenartige Schachprobleme" (only available in German) which all members of the Schwalbe received as a present. Interestingly, he also listed several challenges for the readers — without timely limitation and each awarded with Euro 100! Four of the seventeen tasks have already been solved in 2010. You can find these solutions here (the last four diagrams).

Three composing challenges were mentioned by both Rothwell and Keym. Let's have a look at them:

1. Double square vacation with both white castlings in a moremover

1.1

Thomas Rainer Dawson

Chess Amateur, 1923

#3

(9+7)

1.2

Andreas Thoma

König und Turm, 2003

#4

(13+10)

Sam Loyd was the first to show the double square vacation by castling. This was already achieved in 1877 but only with an illegal position. I won't bother you with that, for I prefer to give you a correct problem which you see in diagram 1.1.

You may criticize the rather weak key, but consider that the first step is always proving the feasibility. After that is done you can look for improvements. However, there is the slight weakness that the square vacation of e1 is used by the wQ twice. A perfect setting would need the additional variation 3. Ne1 after 2. 0-0-0. This is what we still are trying to construct.

Conjecture: It is impossible to construct a moremover showing double square vacation of a1, e1, h1 by white castling on both sides whereby the square vacation of e1 has to be used by two different white pieces.

2. Oudot task in the orthodox helpmate

2.1

Marcel Tribowski

StrateGems, 2002

2nd Prize

h=9

(5+10)

2.2

Reinhardt Fiebig

harmonie, September 2005

h#9

(2+12)

A famous, yet unachieved, helpmate task is the so-called Oudot task which is named after the French composer Jean Oudot. It demands the promotion of three black pawns to queen in a single solution in an orthodox helpmate. The minimum length of such a composition is nine moves, as it takes at least three moves for each pawn to substantiate its promotion to a black queen.

The earliest attempt in five moves dates back to 1965 when Jenö Ban used six promoted pieces. His solution is often used to demonstrate the task. Since then, composers gradually managed to reduce the amount of promoted pieces. The best result so far is diagram 3.2 with only two promoted pieces:1. b5 e4 2. b4 e5 3. bxc3 e6 4. cxd2 e7 5. dxe1=N e8=N#.

Conjecture: It is impossible to construct an orthodox helpmate in five with a black and a white N-excelsior.

Whereas Keym awards the 100 Euros only for compositions meeting the original requirements of the first two tasks mentioned here, he obviously assumes that the conjecture for the third task is true. He offers 100 Euros for the first construction with only one promoted piece.

Solving these or other tasks might appear to be impossible, the more if one reads how many brilliant composers already made so many incorrect attempts. Still, the very same was true for the famous Babson task. After many decades, someone finally came up with a solution, but this was not one of the big names! Leonid Yarosh was virtually unknown until 1983 when he published the first correct Babson. So, don't give up — at least not before someone proved the impossibility.